This section is intended to introduce the reader to various aspects of the art that may be related to various aspects of the present invention. The following discussion is intended to provide information to facilitate a better understanding of the present invention. Accordingly, it should be understood that statements in the following discussion are to be read in this light, and not as admissions of prior art.
Transit-time chordal ultrasonic meters determine volumetric flow by numerically integrating fluid velocities measured on two, four or more chordal paths. In larger meters the results of this numerical integration of measured velocities usually accord closely with the actual volumetric flow—meter factors that account for the difference between theoretical and actual flow rates typically will lie within a few tenths of a percent of 1.000.
In meters having smaller internal diameters with larger transducer cavities the agreement between the theoretical and actual is not as good when Reynolds Numbers are below about 500,000. Deviations approach 1%, and vary with the Reynolds Number. FIG. 1 illustrates the problem. It plots meter factor data for a collection of meters ranging in internal diameter from 4 inches to 10 inches against Reynolds Number. At a Reynolds Number of about 500,000, the meter factors are close to theoretical (i.e., 1.000) but as Reynolds Number diminishes from this figure, the departure from theory increases to a maximum of about 0.8% at Reynolds Numbers in the 30,000 to 50,000 range.
Experimental data—specifically the response of the chordal velocities to changes in Reynolds Number—show that the cause of this non-linear response of meter factor to changing Reynolds Number has to do with the response of the flow field (the fluid velocity profile) to the geometry of the transducer cavities, such as the geometry for a typical 4 path meter in FIG. 2. At low to intermediate Reynolds Numbers, components of the fluid velocity enter the cavities, projecting onto the acoustic paths in such a way as to cause the fluid velocity seen by a path to be higher than that which would prevail if the cavities did not exist. The effect is greatest on chords furthest from the centerline. As can he seen in FIG. 2 the geometry of the downstream cavities for the outer paths of a 4-path meter would particularly lend itself to such a response.
The degree to which this distortion of the flow field occurs depends on Reynolds Number, probably because the attachment (or separation) of the boundary layer in the vicinity of the cavities depends on the relative magnitudes of the local inertial and viscous forces. At any rate, the higher-than-expected chordal velocities require meter factors less than the theoretical (1.000) to correct them, the amount of the correction varying with Reynolds Number.
The nonlinear dependence of meter factor on Reynolds Number presents a calibration problem. If such a meter is applied to the accurate measurement of the flows of products have differing viscosities or if the application covers a wide range of flows, the range of Reynolds number to which that meter will be subjected will be broad and is likely to include the range in which the meter factor is sensitive to the value of the Reynolds Number. Accordingly, the meter must be calibrated in a facility that has the capability to vary Reynolds Number over a wide range so as to establish the Meter Factor-Reynolds Number relationship with precision. Such facilities are rare; only two are known to exist in the United States.
Furthermore, the algorithm for the meter itself must include a provision for a Reynolds Number correction, and must receive an input from which it can determine kinematic viscosity (the other components of Reynolds Number, internal diameter and fluid velocity, are already available in the meter). Fluid viscosity is not easy to measure and is usually inferred from other variables, such as fluid density or sound velocity and temperature. The accuracy with which these variables are measured and the accuracy of the empirical relationship between them and the fluid viscosity affects the accuracy of the Reynolds number determination, and therefore the accuracy of the adjustment to the “raw” meter factor.
The dependence of meter factor, in meters of 10 inch internal diameter and smaller, on Reynolds Number thus leads to increased expense (to perform the special calibrations needed to characterize the meter factor) as well as to reduced accuracy (because of the uncertainties associated with the correction of the meter factor with a Reynolds Number inferred from data in the field).